The Pareto Law remains to be one of the great mysteries of our time. To our opinion, well known  applicability of the Pareto relationship in different sciences  indicates the existence in Nature some unknown earlier statistical “law of large numbers” with the statistical weight Ω═N!/Z₁Z₂ , where N=∑_m K_m , K_m=n_mm , Z₁=∏_m (m!)^n_m, Z₂=∏_m (K_m)!.    The Stirling approximations N!≈(N/e)^N≈∏_m (N/e)^K_m and (m!)ⁿ_m ≈(m/e)^K_m  lead to Ω=∏_m Ω_m , where Ω_m=(N/m)^K_m/(K_m!). This  Maxwell-Gibbs form demonstrates that K_m=n_mm-subnumbers are not fermions or bosons. We would name them  “competitors”. After approximation K_m !≈(K_m/e)^K_m we receive general entropy S=lnΩ−∑_mn_mmln(Ne/m²n_m). By three conditions N=∑_mn_mm=const, M=∑_mn_m=const, R=∑_mR_mn_m=const   the requirement S→max gives the spectrum n_m=Nm^-2exp[-a₁-(a₂+R_m)/m].  At  a₂=0 and  R_m=a₃m we have the Pareto law in differential,  n_m=Am^-2 , and integral, N(>m)=A[(1/m)-(1/m_max)], forms. This result settles the problem of the Pareto law substantiation.

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